论文标题
估计多变量纯跳跃半明星的二次变化
On estimation of quadratic variation for multivariate pure jump semimartingales
论文作者
论文摘要
在本文中，我们介绍了对多变量对称$β$稳定过程的实现二次变异的渐近分析，（0,2）$ $β\ $β\ $β\ in（0,2）$和某些纯净的跳跃半模拟。主要重点是用于实现二次变化及其频谱的功能极限定理的推导。我们将表明，当原始过程是对称的$β$稳定时，限制过程是矩阵值$β$稳定的lévy过程，而在对称$β$稳定的Motions方面，限制为$β$ - 稳定。这些渐近结果主要与工作[5]有关，该工作研究了该问题的单变量版本。此外，我们将展示对二次变异矩阵的特征值和特征向量估计的影响，这是原理分析的有用结果。最后，我们提出在Lévy环境中进行一致的子采样程序，以获得置信区。
In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $β$-stable Lévy processes, $β\in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of functional limit theorems for the realised quadratic variation and its spectrum. We will show that the limiting process is a matrix-valued $β$-stable Lévy process when the original process is symmetric $β$-stable, while the limit is conditionally $β$-stable in case of integrals with respect to symmetric $β$-stable motions. These asymptotic results are mostly related to the work [5], which investigates the univariate version of the problem. Furthermore, we will show the implications for estimation of eigenvalues and eigenvectors of the quadratic variation matrix, which is a useful result for the principle component analysis. Finally, we propose a consistent subsampling procedure in the Lévy setting to obtain confidence regions.
